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Improving MCMC, using efficient importance sampling

  • Liesenfeld, Roman
  • Richard, Jean-François

A generic Markov Chain Monte Carlo (MCMC) framework, based upon Efficient Importance Sampling (EIS) is developed, which can be used for the analysis of a wide range of econometric models involving integrals without analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components, such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC-EIS approach is illustrated with simple univariate integration problems, and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2008)
Issue (Month): 2 (December)
Pages: 272-288

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Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:272-288
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  2. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
  3. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
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  8. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  9. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
  10. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Estimation of Dynamic Bivariate Mixture Models: Comments on Watanabe (2000)," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 570-76, October.
  11. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  12. John F. Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  13. Neil Shephard & Siem Jan Koopman, 2002. "Testing the assumptions behind the use of importance sampling," Economics Series Working Papers 2002-W17, University of Oxford, Department of Economics.
  14. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
  15. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  16. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
  17. repec:pit:wpaper:321 is not listed on IDEAS
  18. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," CORE Discussion Papers 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  19. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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